You have researched your dream around-the-world vacation and determined that the total cost of the vacation will be $44,000. You feel you can earn an APR of 10.3 percent compounded monthly and plan to save $560 per month until you reach your goal. How many years will it be until you reach your goal and enjoy your well-deserved vacation

It will take about 20 years

Explanation:

Sinking Fund involves saving an series of equal amount periodically invested at certain rate of interest to accumulate a target amount in the future. The target amount might be to finance a particular project - a vacation in this case.

Where an equal deposit is invested the sum accumulated (deposit plus interest earned) at the end of the final period is known as the Future Value (FV) of the sinking fund. The future value in this scenario = $44,000

The FV is determined as follows:

FV = Equal monthly deposit × Monthly Annuity factor

where FV- future value, A- equal cash deposit, r-rate of return, n- number of years.

A= 560, r = 10.3, n= ?

Monthly Annuity factor = 44,000/560 = 78.571

Monthly interest rate = 10.3/12=0.8583

Annuity monthly annuity factor =( (1+r)^n - 1 )/r

(1.008583^12n -1)/0.08583= 78.571

cross multiply

78.571×0.08583= 1.008583^12n -1

6.7437= 1.008583^12n -1

6.7437 + 1 = 1.008583^12n

7.7437=  1.008583^12n

find log of both sides

12n = log 7.7437/log  1.008583

12n = 239.50

n= 239.50/12 = 19.9 years.

Approximately 20 years

It will take about 20 years

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